Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
444 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 107 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #20272702 | C2 | direct (N × H) |
| 5. C22×Dic212 | C4 | semidirect |
| 10. #16810881 | C4 | semidirect |
| 12. C2×#13133149 | C4 | semidirect |
| 24. C2×Dic212 | C2×C4 | semidirect |
| 36. #13133149 | C2×C4 | semidirect |
| 169. C2×C53 | #1340 | semidirect |
| 186. C53 | C2×#1340 | semidirect |
| 331. C2 | #20272702 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810881 | 2 |
| C2×#16810405 | 2 |
| #20272702 | 2 |
| C2×C53×H(3,ℤ/4) | 2 |
| C2×#1340 | 53 |